WORKSHOP REPORT
ASTRODYNAMICS OF INTERCEPTION
16 January 1992
Claude Phipps (chair), Los Alamos National Laboratory
Edward Bowell, Lowell Observatory
James Burke, The Planetary Society
Joseph Gurley, Hughes Aircraft Company
Eleanor Helin, Caltech Jet Propulsion Laboratory
Jack Hills, Los Alamos National Laboratory
Brian Marsden, Smithsonian Astrophysical Observatory
Introduction
There exists a spectrum of possibilities for impact of near-Earth objects (NEOs) with Earth, ranging
from an overwhelming, unpredicted disaster through objects whose orbits are so well-known that
threats from them can be mitigated with certainty.
Warning time is the distinguishing factor among these different cases. Our interest does not exceed
many decades on the high side, and is limited on the low side by that time [twarning < a few days] for
which no astrodynamic response is possible.
Table I shows the way we divided the problem for consideration, beginning at the most favorable
extreme, and working toward the less predictable cases in our discussion of interception.
Case 1
These are Earth-crossing asteroids (ECAs) with well-determined orbits. Error ellipsoid dimensions
for the predicted Earth encounter are of the order RE (or smaller), and, therefore, we can predict
with reasonable confidence which apparitions will bring the asteroid into Earth impact. Here, we
can predict positions precisely enough to allow warning times of decades or even centuries.
Some of the threatening objects are in highly inclined, highly elliptical orbits, and will require large
ΔVs to intercept, but we can afford to use minimum-energy orbits. We can use the available time to
carry out sufficient precursor missions to remove most uncertainties from the intercept. If Vintercept
of 25 km/s is acceptable, then it would be possible to fly a mission with a C3 of 1 or 2 (km/s)2. We
can intercept the object at the intersection of the asteroid and Earth’s orbits. Impulse is best
imparted to asteroids other than Aten-types at perihelion, unless that is too close to the Sun for
comfort. In the case of Aten-type asteroids, interaction is best at aphelion.
It is clear that programs treating Case 1 will have beneficial spinoffs for other NASA programs.
Case 2
These are newly discovered ECAs or short-period comets with significant non-gravitational forces
having unpredictable temporal variation. In either case, orbital uncertainty reduces the lead time
with which we can predict probable Earth impact to a few years.
Newly discovered ECAs have less certain orbits. Such objects will probably be faint, so the
response must be more urgent.
Every available means should be employed to refine the orbit. Once determined to be a threat, much
higher intercept velocities are likely to be required in this case. The C3 needed could be enormously
higher than in Case 1, and there is not the luxury of using an extra orbit to get a planetary flyby. On
arrival at the target, the impulse delivered will be an order of magnitude larger than for Case 1. It is
possible that a launch window might not exist for some reason, putting the object into Category 3.
Success at the first attempt is critical for the intercept mission in this case, since failure may also
have the consequence of changing the interaction into Case 3.
Case 3
Here the object is first identified as a threat when it is on a collision course with Earth. The object is
typically a long-period comet approaching Earth. The most propitious scenario is discovery at a
range of 10 AU at V=22 mag. It is likely to be 10 km or more in size to achieve this optimum case.
At 5AU, much of the comet’s light will be in the coma, making discovery much easier.
Newly discovered ECAs in this category are likely to be small bodies (less than a few hundred
meters across), providing an adequate search for ECAs has been carried out previously.
Response in Case 3 requires an entirely different approach.
Launch is with shortest response time possible, and with the highest feasible velocity. Interception
range is 0.1 – 1 AU, with a C3 of 100 (km/s)2, probably associated with a flyout time of about 1
week. The zone of feasible interception is probably within 0.1 AU in this case, whatever the
intruder’s orbit [see the Appendix to this report].
Case 4
With the present state of observational activity, this is by far the most likely scenario! The impactor
could be a 5-km ECA. Extreme responses should be considered for this case, since astrodynamic
response is very difficult or impossible.
APPENDIX
by
Joseph Gurley
The unique feature of the astrodynamic problem of intercepting an Earth-impact-threatening NEO is
that the orbits of the NEO and of the Earth intersect at the ascending or descending node of the NEO
orbit where the impact is predicted to occur.
Figure A1 shows a locally optimal maneuver to achieve a rendezvous with the NEO, starting from a
low Earth orbit (LEO). A large impulse, essentially equal to the difference between the predicted
Earth impact velocity of the NEO and the Earth orbital velocity of the spacecraft, is applied at the
time Earth passes the nodal longitude. This injects the spacecraft into an orbit approximately
matching that of the NEO, except for orbital phase and a small orbital period mismatch. This period
difference is chosen so as to cause the two bodies to drift together, at which point an orbit trim
maneuver completes the rendezvous. The total ΔV for this mission is typically in the range 7 – 18
km/s. The case 2 threat, with a warning time of only a few years, may require this type of
interaction, perhaps modified to increase the drift rate at the cost of a higher orbit trim ΔV; this
modification will decrease the time spent in the drift phase of the mission.
Figure A2 shows an alternative interception trajectory which reduces the mission ΔV by relaxing
the rendezvous requirement and using a high-velocity approach, typically in the range 10 – 20 km/s.
The interceptor is injected into a heliocentric orbit with a period slightly under or slightly over one
year, at a point near the node of the NEO orbit (the point where impact with Earth is predicted to
occur). Interception occurs at that same nodal point, several years later. A slightly modified version
of this strategy may be useful against Case 2 threats, where mission ΔV is to be minimized, and the
time available is tightly constrained.
An alternative low-ΔV strategy (Figure A3) uses multiple planetary gravity assist maneuvers to
approximate a globally optimal transfer from LEO to a rendezvous with the target asteroid. This
strategy is appropriate for high-impact-velocity Case 1 (long warning time) threats, whenever the
defensive system requires either a rendezvous with the target object, or an interception far from
Earth’s orbit, e.g., at the perihelion point. For a rendezvous, the final gravity assist maneuver will
generally be an Earth flyby at the node of the NEO orbit, to inject the spacecraft into a matching
rendezvous orbit. The mission ΔV for this type of trajectory is the sum of the impulse needed to
inject the vehicle into an interplanetary trajectory to the first flyby planet (probably Venus or Mars:
estimated ΔV = 4 – 5 km/s), and a small amount (probably < 0.5 km/s) for guidance and orbit trim
maneuvers.
TABLE I: CASE DEFINITION
Case
1. Well-defined orbits
twarning
Decades
Long-term, VEGAtype missions
Years
Urgent response
without much room
for error
– Precursor missions are strongly
advisable for detailed
evaluation
2. More uncertain orbits
Action
– Luxury of precursor mission
may be absent
Probability of
Scenario for 1-km
objects
Now
Future
5%
95%
Interaction
Distance
(AU)
Target ΔV
(cm/s)
Object
2
1
ECAs only
2
10 – 100
(more error) Short-period
comets
– Intermediate warning time (but
still urgent)
(less error)
– Object motion is affected by
nongravitational forces
3. Immediate Threat
Months
– Best scenario: discovery at 10
AU
0.1
(comet)
Continue to refine
the orbit
– Discovery initiates emergency
4. You’re hit before you know it!
Every available
engineering measure
0 – Days
Pray
0.1 – 1
(ECA)
95%
5%
0
> 1000
Newlydiscovered
ECAs
Long-period
comets
Small, newly
discovered
ECAs
Long-period
comets &
unknown ECAs